The Twelfth OMISAR Workshop on Ocean Models
Comparison and study of WEN Model and SWAN
Model
1
1
Hu Wei , Changlong Guan
ABSTRACT
This paper is concerned with the comparison and study of WEN Model, a
new approach to wave modeling, and a typical wave action model [Simulation
Waves Nearshore(SWAN)]. Through different model cases, including the
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modeling in the Bohai sea ( 117 32′E − 122 16′E , 37 6′N − 40 56′N ) and the
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modeling in the Northwest Pacific ocean( 119 E − 129 E , 20 N − 30 N ) of
both WEN and SWAN，simulated significant wave height and significant wave
period of the two models are compared with measured data, and the wave
spectrum of the two models are also compared. From the comparison result,
we include that the computed spectra of WEN and SWAN model have the
similar spectral shape, and the simulated significant wave height by WEN
model generally agrees with that observed, but has deviation from the
observed data when wave height is small.
INTRODUCTION
The state of the art in medium- and large-scale wave modeling today is the
third-generation wave model, which solves the spectral action balance equation without
prior assumption of spectral shape. The performance of these models has been
demonstrated in numerous works. Also uncertainty involved in the computation of the
source terms of the governing equation has been mentioned (Tolman and Chalikov,
1996).
Wen at al, (1999) extensively argued the deficiencies of third-generation wave
model, including incompatibility and uncertainty in the computation of source terms,
limitation in model’s performance， inaccuracy caused by the source term of nonlinear
wave-wave interaction and difficulty of improvement, and proposed a new approach to
wave modeling.
The main purpose of this study is to get the performance of WEN model and to
compare it with the third-generation SWAN model.
1
Institute of Physical Oceanography, Ocean University of China, Qingdao 266003
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MODEL DESCRIPTION
SWAN MODEL
In this study, the widely used coastal wave model—SWAN (Booij et al., 1999;
version 40.31) was employed. SWAN is a third-generation wave model which was
designed specifically to simulate coastal ocean waves, compared with other third –
generation models such as WAM and WAVEWATCH which are developed specifically
for simulating waves in the deep water.
The governing equation of SWAN is the wave action balance equation
∂N ∂Cg , x N ∂C g , y N ∂C g ,σ N ∂Cg ,θ N S
+
+
+
+
= ,
(1)
∂t
∂x
∂y
∂σ
∂θ
σ
where N is the wave action density; σ is the relative frequency; θ is the wave
direction; Cg is the propagation speed in ( x, y , σ ,θ ) space; and S is the total of
source/sink terms expressed as wave energy density.
For SWAN, the source terms are expressed by
S = Sin + Sds ,w + Sds ,b + Snl 4 + Snl 3
(2)
The terms in the right-hand side of the equation respectively mean the wind input,
whitecapping, bottom friction, quadruplet wave-wave interactions, and triad wave-wave
interactions. The terms of bottom friction and triad wave-wave interaction can be
neglected in deep water calculations.
WEN MODEL
In WEN model, the wave spectrum is considered as a combination of wind-wave
and swell components. The wind-wave component is defined as one, which receives
energy directly from the wind, and from other components through nonlinear wave-wave
interaction. The swell component, on the other hand, receives no energy from the wind
and receives on energy through the nonlinear interaction. All components are to be
computed from spectral transport equation,
v
∂F
(3)
+ ∇g(Cg F ) = S
∂t
by employing the splitting scheme
F ′ − Fi
(4)
=S
∆t
v
Fi +1 − F ′
+ ∇g(C g F ′) = 0
(5)
∆t
Where Fi and Fi +1 are the spectral values of a wave component at two
successive time steps i and i + 1 respectively, the length of the time interval being
∆t .
For the wind-wave component, the value of F ′ is determined by the empirical
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formula of wave growth and a presupposed spectral form. F ′ in Eq.(4) can be put in
the form
F ′ = F (ω ,θ ) t =t +∆t
(6)
e
where te is called equivalent time representing the time required for the spectral
component growing to the magnitude Fi under the constant wind speed over the time
interval ∆t .
The relationship of the zeroth spectral moment m0 with time under constant
wind condition was determined by Wen at al, (1999)
U 3.09 0.91
141g 0.344 d 0.8
0.91
2
t
k
d
tanh
(1.4
)
tanh
(7)
s
1.09
U 1.14t 0.456 tanh 0.456 (1.4k s d )
2 g
ω
1
k s = 1.21 0
(8)
g tanh( k s d )
where m0 is the zeroth spectral moment; d is water depth; U is the wind
speed at 10 meter height; g is the acceleration of gravity; ω0 is the peak frequency,
and k s is the wave number of significant wave.
m0 = 8.54 × 10−8
The presupposed spectral shape is proposed by Wen et al. (1995)
For the computation of swell component, the source function in Eq.(4)
S = Sds + Sdb
(9)
The terms in the right-hand side of the equation respectively mean dissipation by
turbulent viscosity and dissipation by bottom friction.
MODEL PERFORMANCE
Several cases of both WEN and SWAN modeling are carried out in the Bohai
Sea. The observed data is positioned at the point ( 118o48′32′′E ,38o13′8′′ N ) with water
depth of 8m (shown in fig.1). The observed wave data was recorded from the time
period of 1998.04.22.20—1998.04.25.02(55 hours) and 1999.04.02.14 —1999.04.02.14
(38 hours). The data was sampled at every 1 hour. The computational region of the
model extends from 117o32′E
to 122o16′E
in longitude and from 37o6′ N
to
40 56′ N in latitude. The spatial resolution is set to be 2′ for both longitude and
o
latitude, and the time step for the computation is set to be 900 s for the two models. The
simulated significant wave height and significant wave period shown in fig.2 and fig.3
agree with the observed data. The significant wave height modeled by WEN is lower
than simulated by SWAN, and the significant wave period modeled by WEN is longer
than SWAN got. The computed spectra of WEN and SWAN model have the similar
spectral shape (shown in fig. 4).
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Cases of the modeling are also carried out in the Northwest Pacific ocean. The
buoy station in the model domain is located at 121.923o E , 25.096o N (shown in fig. 5).
The Computational region covers from 115o E to 132o E in longitude and from 15o N
to 35o N in latitude. Spatial resolution is set to be 1/ 6o for both longitude and latitude,
and time step is set to be 1200 s for both SWAN and WEN model. The comparison of
simulated significant wave height with observed during the period of
2003.6－2003.12
is shown in fig. 6. The significant wave height modeled by both of WEN and SWAN
generally agree with that observed by buoy
Gathering all the simulated and observed significant wave height data (shown in fig.
7－9), we get that when wave height is lower than about 1.0 meter, significant wave
height simulated by WEN model is lower than that observed, and also has difference
with that simulated by SWAN. WEN model performs well except a few points (shown in
fig. 7) when the wave height is higher than about 1.0 meter.
CONCLUSION
WEN model, as a new approach of wave modeling, has been validated in our
numerical experiments, which is still not full tested and developed like the
third-generation wave models. In the numerical experiments, the simulated significant
wave height by WEN model generally agrees with that observed, but has deviation from
the observed data when wave height is small. It needs more tests and more
improvements to get better performance.
REFERENCES
Booij, N., R.C.Ris, and L. H. Holthuijsen, 1999: A third-generation wave model for
coastal regions. 1. Model description and validation, J, Geophys, Res,.104,
7649-7666
Tolman H L and Chalikov D. Source terms in a third-generation wind-wave model. J
Phys Oceanogr, 1996, 26; 2497-2518
WAMDI Group, 1988. The WAM model-a third generation ocean wave prediction model.
J. Phys. Oceanogr.,18, 1775-1810.
Wen S C, Wu K J, Guan C L, et al. A proposed directional function and wind-wave
directianl spectrum. Acta Oceanol Sinica, 1995, 14; 155-166
Wen S C, Qian C C,Ye A L. et al., Wave modeling based on an adopted wind-wave
spectrum, J. Ocean Univ. Qingdao, 1999, 29:345.
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Fig. 1 Computational region in Bohai sea and the observe location
Fig. 2 Comparison of hs(m), ts(s) among measured, WEN and SWAN simulated. Time
is from 1998.04.22:20 to 1998.04.25:02
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Fig. 3 Comparison of hs(m), ts(s) among measured, WEN and SWAN simulated. Time
is from 1999.04.01.00 to 1999.04.02.14
Fig. 4 Comparison of frequency spectra between SWAN and WEN simulated in Bohai
sea at 1998.04.23.20, 1998.04.24.14, 1999.04.01.12 and 1999.04.02.00.
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Fig. 5 Computation region in Northwest Pacific ocean and bouy Longdong location.
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Fig. 6 Comparison of hs(m) among bouy observed, WEN and SWAN simulated during
the period form 2003.06 to 2003.12 seven months.
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Fig. 7 The comparison of hs between WEN modeled and observed
Fig. 8 The comparison of hs between WEN and SWAN simulated
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Fig. 9 The comparison of hs between SWAN modeled and observed
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